Question

Find the value of $\frac{\cos \left(90°-\mathrm{\theta }\right)\cos \mathrm{\theta }}{\cot \mathrm{\theta }}-1$.

Answer 1

Dear student,

$$\begin{gathered} Wehave, \\ \frac{\cos \left(90°-\theta \right)\cos \theta }{cot\theta }-1 \\ =\frac{\sin \theta \cos \theta }{cot\theta }-1 \\ =\frac{\sin \theta \cancel{\cos \theta }}{{\displaystyle \frac{\cancel{\cos \theta }}{\sin \theta }}}-1 \\ ={\sin }^2\theta -1 \\ =-\left(1-{\sin }^2\theta \right) \\ =-{\cos }^2\theta \end{gathered}$$

Regards